THEl1PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

Tadeusz Antczak ()
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Tadeusz Antczak: Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Asia-Pacific Journal of Operational Research (APJOR), 2010, vol. 27, issue 05, 559-576

Abstract: In this paper, some new results on thel1exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via thel1exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitabler-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with thel1exact penalty function is also established.

Keywords: Penalized optimization problem; l1exact penalty function; exact penalty function method; r-invex function with respect to η (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0217595910002855

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